Contributor
Posts: 60

# Comparison of two populations

Hi All,

I have to compare two populations and find whether the means of two population are statistically different.

For example, Population 1 has 10 physics students and population 2 has 100 biology students. I have marks of every student in both population. I need to compare the means of both these population(not samples but whole population) and find whether they are different. Which test statistic can be used to compare these two population for the given scenario?

Thanks,

Saravanan

Posts: 5,521

## Re: Comparison of two populations

Posted in reply to Saravanan

If you know all the marks from entire populations then the average mark is the TRUE mean. No uncertainty, no statistical test, no assumptions required. Use proc means or proc sql or proc tabulate or even proc report to compute averages, and you are done! You would need statistics if your classes were considered samples from larger populations.

PG

PG
Contributor
Posts: 60

## Re: Comparison of two populations

Thank you so much for the reply. It was very helpful. I did follow this approach.

Saravanan

Super User
Posts: 23,663

## Re: Comparison of two populations

Posted in reply to Saravanan

The average is calculated the same between sample and population, but the standard deviation is different. (n for pop vs n-1 in sample for the denominator). Using a combination of proc means and proc t-test you can use a simple T-Test. This assumes your normality assumptions are met, with the hugely different sample sizes it probably isn't and probably isn't a fair comparison regardless.

Calculate the summary values from proc means with the vardef=n option to calculate the standard deviation with a denominator of N rather than N=1.

Then you can use Proc T-Test to with Summary Stats, see example below

SAS/STAT(R) 9.2 User's Guide, Second Edition

Posts: 2,655

## Re: Comparison of two populations

On this one, I vote for 's approach, if these are the whole populations AND there is no generalization to future students.
The means are either the same or different.

Otherwise, consider that these are a sample of all possible students and proceed as if they were samples.  It is really important to distinguish what inferential value is to be placed on the values obtained.

Steve Denham

Contributor
Posts: 60

## Re: Comparison of two populations

Posted in reply to SteveDenham

Thank you. I did follow Pierre Gagnon`s approach.

Saravanan

Contributor
Posts: 60

## Re: Comparison of two populations

Thank you for the reply. This was very informative.

Saravanan

Discussion stats
• 6 replies
• 289 views
• 0 likes
• 4 in conversation